[R-sig-ME] random slope model overinflate CI?s

[Greg Guerin]

Hello Juan,

I have trouble following the second half of the message, so perhaps I am missing your point, but responding to this part:

"Digging into the experimental data I realized the convenience of including  *fish_length* as random slope. After this change, the diagnostic criteria (AIC, BIC)  improved a lot, compared to the first modeling approach but the winner model only  gave the intercept as significant fixed effect:

mod45<-glmer(prop~1+(fish_length|haul),family=binomial,data=X.red,nAGQ=1,weights=ntotal)"

The reason this model gave only intercept as a fixed effect is that only intercept was specified as a fixed effect. To include as both  random and fixed, you would need to specify it twice, along the lines of a ~ b + (1+b|c)

Greg

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Dr Greg Guerin
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The University of Adelaide
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greg.guerin at adelaide.edu.au
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Date: Fri, 07 Feb 2014 18:32:55 +0100
From: Juan Santos <juan.santos at ti.bund.de>
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] random slope model overinflate CI?s
Message-ID: <52F518C7.60308 at ti.bund.de>
Content-Type: text/plain

     Hello,

I ??m dealing with a  fishing dataset obtained from a research cruise two
trawl gears were fishing in paralel (twin trawling) during each of the
fishing realizations (hauls) carried out. The response variable is the
proportion of catches in the test gear prop=test/(test+reference).
therefore:

  # prop=0.5 can be interpreted as  both  gears having the  same fishing
efficiency on a given fish species
  # prop<0.5 means therefore less catch efficiency in the test gear.

The dataset contains a total of 14 hauls balanced in two different test
*gear_setup* (setup1 (7 hauls) setup2 (7hauls)). Caught fishes were
counted and measured (*fish_length*)

The aim of the modeling approach was:

-To evaluate if fish length size or gear setup significantly affects the
response *prpp* .

Proposed model and first approach:

A mixed modeling approach using glmer(). Haul as  random intercept. The
best model of this random intercept approach was:

mod5<-glmer(prop~gear_setup*fish_length+(1|haul),family=binomial,data=X.red,nAGQ=1,weights=ntotal)

              Df    AIC    BIC  logLik deviance   Chisq Chi Df Pr(>Chisq)
mod5  4 2067.4  2083.6 -1029.7   2059.4  7.3644      0  < 2.2e-16 ***

Random effects:

  Groups Name        Variance Std.Dev.
  haul   (Intercept)      0.2131   0.4617
Number of obs: 428, groups: haul, 14

Fixed effects:
                          Estimate Std. Error z value Pr(>|z|)
(Intercept)    -3.55598    0.29711 -11.969  < 2e-16 ***
setup2           1.60421    0.42128   3.808  0.00014 ***
fish_length    0.08660    0.01005   8.613  < 2e-16 ***
setup2:l        -0.06390    0.01409  -4.534  5.8e-06 ***


Second  approach:

Digging into the experimental data I realized the convenience of
including  *fish_length* as random slope. After this change, the
diagnostic criteria (AIC, BIC)  improved a lot, compared to the first
modeling approach but the winner model only  gave the intercept as
significant fixed effect:

mod45<-glmer(prop~1+(fish_length|haul),family=binomial,data=X.red,nAGQ=1,weights=ntotal)

       AIC       BIC              logLik         deviance
1876.6   1892.9283 -934.3459 1868.6918

Random effects:
  Groups Name        Variance Std.Dev. Corr
  haul   (Intercept)   6.97522    2.6411
fish_length             0.01171   0.1082   -0.98
Number of obs: 428, groups: haul, 14

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)
(Intercept)  -1.4575     0.1292  -11.28   <2e-16 ***

As I understand this model output, Including the  *fish_length* as
random slope mask any fixed effect included in the model, since  the
functional form of *prop* conditioned to *fish_length*  varied a lot
between hauls. The problem arise when estimating the  confidence
intervals from this model;


   prop.mu       F_lci      F_uci      R_lci            R_uci
            0.18    0.15      0.23         0.001        0.97


where *prop.mu* is the expected *prop* estimated in mod45; *F_* denotes
the CI estimated using the fixed effect uncertainity, and *R_*
represents the confidence intervals adding the uncertainity produced by
the betweenn haul variation (sigma_2= 6.97522) . The *R_ * band is
unexpectely high ranging  from 0.001 to 0.97, crossing by far the
reference value of p=0.5 (equal catches).

I interpret this results as follows:

- Altough during the experiment there was a  significant catch reduction
in test gear (0.18[0.15-0.23 ]), this catch reduction is not significant
if we raise the inference into  a "population of hauls" perpective
(0.18[ 0.001-0.97]).

So the questions are:

1.- Is my interpretation correct?
2.- How can this be possible, when plotting the experimental *prop*
against *fish_length* -plot(prop~fish_length ) -  for each haul
separately , it shows *prop* to  be less than 0.5 for  ~95% of
*fish_length* presented in the catches?

Thank you in advance.



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